Variance and standard deviation of response time averages

It is useful to know the dispersion of the response time data. The variance is a measure of how variable the data is. The square root of the variance is the standard deviation. Assuming the distribution is a normal distribution, you can have the following confidence level:

• 68% that a response time value will fall within the average, plus or minus 1 standard deviation
• 95% that a response time value will fall within the average, plus or minus 2 standard deviations
• 99% that a response time value will fall within the average, plus or minus 3 standard deviations

The data that is saved for variance and standard deviation includes the data that is saved for life-of-connection averages, and the sum of each response time squared for the following data:

• Complete round-trip.
• IP portion of the transaction.
• SNA portion of the transaction. The sum of squares cannot be derived in this case and must be separately maintained.

These values might wrap. It is up to the management application to detect this. The Telnet connection display will indicate the wrapped condition instead of displaying these values or the standard deviation. The typical formula used for variance is:

VARIANCE = SUM((Xi-Xm)**2)/(n-1)

However, that would require keeping all the individual response times to calculate the sum of the squares. The same formula can be expanded and rewritten to not need individual response times. The formula used by Telnet is:

VARIANCE = [SUM(Xi**2) - (SUM(Xi))**2/n]/(n-1)

The values needed in this formula are saved by Telnet for each connection requesting average response time monitoring.